Question : If $a-b=11$ and $ab=24$, then the value of $(a^2+b^2)$ is:
Option 1: 169
Option 2: 37
Option 3: 73
Option 4: 48
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Correct Answer: 169
Solution : Given: $a-b = 11$ and $ab = 24$ Squaring both sides of the equation: $a-b = 11$, we get, $⇒(11)^{2} = a^{2}+b^{2}-2×ab$ Substituting the value of $ab$ in the above equation and get, $⇒121 = a^{2}+b^{2}-48$ $\therefore a^{2}+b^{2} = 169$ Hence, the correct answer is 169.
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Question : If $a-b=2$ and $ab=24$, then what is the value of $a^3-b^3$?
Option 1: 280
Option 2: 124
Option 3: 140
Option 4: 152
Question : If $a + b + c = 0$ and $ab + bc + ca = -11$, then what is the value of $a^2+b^2+c^2$?
Option 1: –11
Option 2: 22
Option 3: 0
Option 4: 11
Question : If cos A = $\frac{5}{13}$, then what is the value of (tan A + cot A)?
Option 1: $\frac{60}{169}$
Option 2: $\frac{109}{169}$
Option 3: $\frac{169}{60}$
Option 4: $\frac{169}{109}$
Question : If a + b + c = 1, ab + bc + ca = –1, and abc = –1, then what is the value of a3 + b3 + c3?
Option 1: 1
Option 2: 5
Option 3: 3
Option 4: 2
Question : The value of [(24 –12) ÷ 4] + [81 – 48 ÷ 12 of 2] is:
Option 1: 67
Option 2: 73
Option 3: 35
Option 4: 82
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